Kid-friendly explanation
Imagine a chocolate bar split into 10 equal squares. Each square is 1 tenth of the whole bar. If you eat 3 squares, you ate 3 tenths, which can be written as the fraction 3/10 or the decimal 0.3. Ten tenths make one whole!
Worked examples with tenths
Example 1 (simpler, upper elementary): Reading and adding tenths
Suppose a juice bottle has 0.4 liters of juice left, and another bottle has 0.3 liters. How much juice is there in all?
First, read each decimal in words. The number 0.4 is "four tenths." The number 0.3 is "three tenths."
To add, line up the decimal points and add the tenths: 0.4 + 0.3.
Four tenths plus three tenths is seven tenths, so 0.4 + 0.3 = 0.7. In words, there are "seven tenths" of a liter of juice.
Example 2 (more advanced, middle grades): Comparing and multiplying tenths
A game app costs $0.70 to download, and a sticker pack costs $0.45. Which costs more, and what is the total cost if both are bought?
First compare the decimals. Both prices show tenths and hundredths: 0.70 has 7 tenths and 0.45 has 4 tenths. Since 7 tenths is more than 4 tenths, 0.70 > 0.45. The game app costs more.
Now find the total cost: 0.70 + 0.45.
Add hundredths: 0 hundredths + 5 hundredths = 5 hundredths. Add tenths: 7 tenths + 4 tenths = 11 tenths, which is 1 whole and 1 tenth. So 0.70 + 0.45 = 1.15.
To see tenths in multiplication, imagine buying 3 copies of a song that costs $0.40 each. Multiply 0.40 × 3. Think of 0.40 as 4 tenths. Three groups of 4 tenths is 12 tenths. Twelve tenths is the same as 1.20, so the total cost is $1.20.
How tenths connect to other decimal skills
Tenths are the first step in understanding decimal place value. The tenths place is always the first digit to the right of the decimal point, and it tells how many tenths of a whole there are.
As work gets more advanced, tenths connect to hundredths and thousandths. For example, 0.3 (three tenths) is the same as 0.30 (three tenths and zero hundredths), and 0.3 is greater than 0.27 because 3 tenths is more than 2 tenths and 7 hundredths together.
Tenths also matter when rounding and estimating. When rounding a decimal to the tenths place, the tenths digit stays or goes up by one depending on the hundredths digit. When estimating square roots or cube roots to the tenths, the tenths place shows how close the estimate is to the exact value.
In operations with decimals, tenths appear in addition, subtraction, multiplication, and division. Lining up decimal points keeps the tenths digits in the same place when adding or subtracting. When multiplying or dividing decimals, thinking about tenths and hundredths helps decide where the decimal point belongs in the answer.
Common mistakes with tenths
- Mixing up tenths and hundredths. A common error is to think 0.4 and 0.40 are different sizes, or to say 0.04 is "four tenths." Correction: 0.4 and 0.40 are the same value (four tenths), and 0.04 is four hundredths, which is much smaller than four tenths.
- Comparing by the number of digits instead of place value. A child might say 0.35 is greater than 0.4 because 35 is greater than 4, so they think 0.35 > 0.4. Correction: compare tenths first; 0.4 has 4 tenths and 0.35 has 3 tenths, so 0.4 > 0.35.
- Ignoring the tenths when rounding. When rounding 3.47 to the tenths place, a child might look at the tenths digit 4 and say the answer is 3.4 without checking the hundredths. Correction: look at the hundredths digit 7; since it is 5 or more, 3.47 rounds to 3.5.
Where tenths show up in everyday life
Tenths appear any time a number has one decimal place. A race time like 3.4 seconds, a distance of 1.7 miles, or a rainfall total of 2.5 inches all use tenths. On a number line marked from 0 to 1 in 10 equal steps, each mark is one tenth of the way between 0 and 1.